Shortest Distance Between Lines MCQs
Shortest Distance Between Lines – MCQs with Answers & Explanations
Class: CBSE Class 12
Subject: Mathematics
Section: Three Dimensional Geometry
Topic: Shortest Distance Between Lines
Exam Focus: CBSE Board Examinations
Subject: Mathematics
Section: Three Dimensional Geometry
Topic: Shortest Distance Between Lines
Exam Focus: CBSE Board Examinations
These Multiple Choice Questions (MCQs) are designed strictly as per the NCERT syllabus, making them ideal for CBSE Class 12 Board Examination practice. Each question includes a detailed concept-clearing explanation.
1. The shortest distance between two skew lines is measured along:
Answer: B
The shortest distance between skew lines lies along their common perpendicular, which is perpendicular to both direction vectors.
The shortest distance between skew lines lies along their common perpendicular, which is perpendicular to both direction vectors.
2. If two lines intersect, their shortest distance is:
Answer: B
Intersecting lines meet at a point, so the minimum distance between them is zero.
Intersecting lines meet at a point, so the minimum distance between them is zero.
3. For parallel lines, shortest distance is:
Answer: C
Parallel lines maintain a fixed perpendicular separation everywhere.
Parallel lines maintain a fixed perpendicular separation everywhere.
4. Shortest distance between skew lines depends on:
Answer: D
Formula uses position vector difference and cross product of direction vectors.
Formula uses position vector difference and cross product of direction vectors.
5. Formula involves magnitude of:
Answer: B
Shortest distance = |(a₂−a₁)·(b₁×b₂)| / |b₁×b₂|.
Shortest distance = |(a₂−a₁)·(b₁×b₂)| / |b₁×b₂|.
6. If cross product of direction vectors is zero, lines are:
Answer: B
Zero cross product ⇒ vectors parallel ⇒ lines parallel or coincident.
Zero cross product ⇒ vectors parallel ⇒ lines parallel or coincident.
7. Shortest distance between intersecting lines using formula gives:
Answer: B
Since numerator becomes zero when lines intersect.
Since numerator becomes zero when lines intersect.
8. Common perpendicular exists only for:
Answer: C
Skew lines neither intersect nor are parallel, so unique common perpendicular exists.
Skew lines neither intersect nor are parallel, so unique common perpendicular exists.
9. Direction of shortest distance is along:
Answer: C
Cross product gives direction perpendicular to both lines.
Cross product gives direction perpendicular to both lines.
10. If lines are perpendicular and intersect, distance is:
Answer: B
Intersection point makes shortest distance zero regardless of angle.
Intersection point makes shortest distance zero regardless of angle.
11. Skew lines lie in:
Answer: C — Skew lines are non-coplanar.
12. Unit of shortest distance is:
Answer: B — It is a linear measurement.
13. Distance between coincident lines:
Answer: A
14. Determinant form is used to compute:
Answer: B
15. If shortest distance = 0, lines:
Answer: B
16. Numerator in formula represents:
Answer: B
17. Denominator represents:
Answer: A
18. Shortest distance is always:
Answer: B
19. If direction ratios proportional, lines:
Answer: B
20. Concept used belongs to:
Answer: B — Topic is from 3D Vector Geometry.